Most biomechanical models used in gait analysis require an estimate of where the hip joint is within the pelvis. The quest for the best equations to do this has become something of a Holy Grail within the gait analysis community. Andriacchi et al. (1980) and Tylkowski (1982) were probably the first to propose methods for estimating its location and Bell, Brand and Peterson (1986) combined these in a method that they claimed predicted the joint centre to within 2.6cm with 95% certainty. At about the same time (1981) a different model was developed from x-ray studies at Newington Children’s Hospital which was incorporated into their clinical gait analysis software (finally published by Davis et al. in 1991).

Some time later Leardini et al. (1991) compared the Bell and Davis models against roentgen stereophotogrammetry and functional methods and found that the models differed quite significantly. Rather than choose one or the other he proposed a new set of equations. A little later Harrington et al. (2007) used MRI scans of a range of healthy children (14) and adults (8) and children with diplegic cerebral palsy (10) and generated another set of equations. A number of validation studies have suggested that those equations perform considerably better than the Davis equations in healthy adults (Sangeux et al., 2011, Sangeux et al. 2014) and children with cerebral palsy (Peters et al., 2012). These have also suggested that Harrington’s equations generally work as well, or better, than modern functional methods.

One of the problems of the methods (highlighted by Sangeux last year) was that the equations scale the hip joint centre to measures of pelvic width (from one ASIS to the other) and depth (from the ASIS to the PSIS). Errors in measuring these, which can be particularly tricky in more obese subjects, can propagate to the hip joint centre estimates. It would be much better to scale to a measure that could be made more accurately such as clinical leg length.

Morgan (Sangeux) discovered that the Victorian Institute for Forensic Medicine had a repository of CT scans which we could access to investigate how well such scaling would work. He and PhD student Reiko Hara found scans of 37 children and 120 adults who had died without any signs of musculoskeletal injury or other abnormality and from which they were able determine the location of the hip joint centre relative to the anatomical landmarks on the pelvis as a function of leg length. As we published last week they found a set of linear functions of leg length that determine the hip joint location as well as the Harrington equations with a mean absolute error of 5.2mm or less in any single direction.

Interestingly (to me) the study showed that despite known differences in general pelvic morphology between males and females there were no appreciable differences in the location of the hip joint centres with respect to the anatomical landmarks (once scaled to leg length) and that age had only a small effect.

The method also means that we have an estimate of the size of the pelvis based on leg length that give us information that we can use when trying to locate where it is in relation to the ASIS and PSIS markers which could be particularly useful in people with higher BMI values.

Morgan has now made the data visible through a new data visualisation resource called Tableau. You can view it there using this link.

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One of the aspects of gait analysis that I didn’t cover in any particular depth in my book was how to select data from a number of trials that is in someway representative of the patient. I think one of the reasons for this is because I couldn’t easily get my hands on any data that illustrated the issues well. In some ways this speaks for itself – in my experience large inter-trial variability, larger enough to affect how we interpret data, is actually quite rare in clinical practice. If the variability is small then it doesn’t really matter what technique you choose.

My personal preference is to avoid the issue altogether by overplotting data from multiple trials on the same graphs (similar to the graphs on the left above but with data from the other side plotted in a different colour as well). In this way you can take into account both the general pattern and the variability when interpreting the data. Some people object that using this technique it can be difficult to appreciate subtle features in individual traces, but there is a real question as to whether you should be even looking at such features if they are not consistent from trace to trace.

Now I’ve started annotating graphs with symbols to identify specific features in the data, however, I find that the combination of symbols and multiple curves can be a bit too messy and have resorted to looking to a single trace that can be taken of as representative. Although alternatives have been proposed I use the average trace. It leads to a little smoothing of the data – which isn’t perfect – but none of the other techniques are perfect either. It was interesting last week to come across a patient’s data that illustrated beautifully the problems of doing this.

You can see the knee and hip traces here with the individual traces overlaid on the left and the averaged data plotted on the right. The problem is with the left knee. You can see that the patient exhibits two distinct patterns of knee movement in early stance (but remarkable repeatability elsewhere in the gait cycle). She either walks with full knee extension in early stance or with quite marked knee flexion. In the fully extended pattern her knee is more posterior and so there is increased hip extension as well (there is an effect on ankle dorsiflexion as well which I haven’t plotted). The average trace for the knee, however, falls well within normal limits and if you only ever looked at that trace you would never know that there was anything wrong with the knee.

None of the methods that are commonly used to generate a representative trace whether they be through picking one particular trace or providing some sort of averaging (mean or median) will result in something that represents the patient. The fundamental reason these don’t work is that this person’s gait is not characterised by one gait pattern, but by two, which she alternates between. It is not possible to understand her walking on a single curve, you need to look at multiple trials.

So although such issues don’t arise very often we don’t have a good way dealing with them in how we plot out or mark-up our data. What is needed is not a way of selecting single trace but a means of indicating that any single trace is unrepresentative. The broad semi-transparent bands on the right hand graphs are supposed to indicate that the trace cannot be appropriately interpreted without referring to the multiple trial data. I’ve now added them to the list of symbols that we use for marking up our graphs.

(PS The idea for a symbol to indicate underlying variability in the multiple trial data was first suggested to me by Sheila Gibbs in Dundee during an early consultation on the Impairment Focussed Interpretation methodology I outline in my book.)

(PPS if you do feel a need to select a representative trace and want to do this systematically then a robust method is presented by Morgan Sangeux in this recent paper. It is however worth noting that in the example he gives in Figure 1 the trace chosen as most representative overall does not give a good indication of the underlying data for either pelvic tilt or foot rotation despite the rigour of the technique.)

Every so often I’m asked about why we tend to do clinical gait analysis barefoot and in AFOs (and shoes). One answer is that the barefoot condition tends to give a better indication of the full extent of a patient’s problems whereas walking in AFOs may be a better indication of how they function in everyday life. Another, however, is that sometimes walking in AFOs can help in identifying which particular impairments are having the most effect on gait. This was certainly the case when, a couple of weeks ago, I was reviewing one of the case studies we often use for teaching purposes but which exhibited features that I had not previously understood.

The analysis is of a seven year old girl with diplegic cerebral palsy (GMFCS III). She can take a few steps unaided but normally walks with a K-walker. We actually tested her in and out of the K-walker barefoot and in shoes and AFOs. the K-walker didn’t make that much difference to the kinematics with either condition so we’ll focus on the two unassisted walking conditions.

Perhaps the most obvious feature of the barefoot data is that she walks right up on her toes in considerable plantarflexion (feature c). The physical examination data shows that plantarflexor contractures (no passive dorsiflexion with knees extended beyond 10° plantarflexion ) can account for some of this but there are also signs of spasticity (from modified Tardieu and Ashworth tests). There is also, however, some suggestion of late (feature b) and reduced (feature a) knee flexion in swing. There is no clear explanation of this from the physical exam although there is a response to the Duncan-Ely test when performed quickly which might indicate some rectus femoris spasticity. Along with these specific findings the assessment indicates generalised weakness, persistent bilateral femoral neck anteversion and some mild tightness of the hip flexors.

The gait analysis with AFOs is quite different. The solid AFOs cast in a neutral position (which might have been assumed to be too aggressive given the physical examination) do appear to be holding the ankle in neutral and substantially limit movement at the ankle (feature h). The pelvis is a little more anteriorly tilted (feature d), possibly to move the centre of mass anteriorly as the new sagittal plane foot alignment will move the centre of pressure anteriorly (the steps were too short to get reliable kinetics). This would also exert a greater external extending moment at the knee which accounts for the hyperextension in late stance (feature g). The increased pelvic tilt leads to increased maximum hip flexion whereas the hyperextension pushes the knee back and maintains maximum peak hip extension. The overall effect is an increased range of movement at the hip (feature e). Perhaps most interestingly though, given that there is a question as to whether the rectus is spastic or not, is that peak knee flexion in swing is essentially normal (feature f). The slope of the knee graph through toe off is if anything a little steeper than normal. Such free flexion of the knee suggests that rectus spasticity is not a problem. Peak knee flexion is still delayed but this is clearly seen to be a consequence of the knee being too extended as it starts to flex in middle single support rather than of any stiffness. In summary, the data from the barefoot condition is inconclusive as to whether rectus femoris spasticity is contributing to the gait pattern but the data from the AFO condition provides quite strong evidence that it is not.

I hope that this has answered the question I posed at the beginning of this post but it does prompt another question – if there is no rectus spasticity then why is peak knee flexion so reduced in the barefoot condition?

I think the answer to this may lie in the observation that if a person is walking on their toes (and in plantarflexion) then it actually requires considerably less knee flexion for clearance in swing than in normal walking. In other words this girl may be showing reduced knee flexion in swing simply because she doesn’t need it when walking barefoot not because there is anything wrong with her knee function.In AFOs the ankle is held in neutral which makes clearance much more difficult and she has no option but to flex the knee more. It is interesting to note that when walking with shoes and AFOs she walks 20% slower than in bare feet and looks considerably less stable and fluent in her movements.

Rather than waste a lot of text in trying to explain why this occurs I’ve recorded a short video using Verne to illustrate that this is the case.

I go into the underlying concepts in relation to normal gait in this screen cast and have explored some of the other consequences of this for those walking in a more crouched gait pattern in this video blog.

Our school Progression Board met on Wednesday and formally approved the award of degrees for the first cohort of students to complete our new masters in clinical movement analysis. I’m sure there is a strong sense of achievement and satisfaction among the students. They’ve worked hard for three years, all of them balancing the requirements of studying alongside their day jobs working in gait analysis services in widely different locations. ~It would be great to post a picture of them all working together but of course they’ve all been studying by distance learning from their own location and the whole group has only ever met in cyberspace (although individuals have visited each other or met at conferences) so instead I’ll insert an advert for anyone who might want to apply for next year!

During the first two years they worked through a programme of learning exercises drawing them into deeper understanding of clinical gait analysis and this year they have focussed on a research project of their own devising. The five projects have been:

How does arm swing change during walking in children with unilateral CP when an orthosis successfully alters foot strike pattern?

Effect of rounded bottom profile shoes on foot clearance in children with stiff knee gait.

A comparison of knee adductor moments from the Plug-in Gait model and a 6 Degrees of freedom model at self-selected and slow walking speeds.

A cross sectional exploratory study to evaluate the validity of the Salford foot model in chronic stroke survivors.

A comparison of the repeatability of two different foot models at self-selected speed in healthy adults.

As well as the obvious success of the students, there has also been a strong sense of achievement for me and the other teaching staff. The programme has grown out of the CMAster project sponsored by the EU Lifelong Learning Programme and in partnership with KU Leuven and VU Amsterdam. We spent two years planning the programme and then three years delivering it so this week really marks the completion of a five year project. We’re all very proud of what we’ve achieved and Adam Shortland, our external examiner, is equally enthusiastic.

There is still time to apply to enrol for this year programme (to start in late September). Further details including how to apply can be found at this link. There is more information, including some material to support those considering enrolling at this site. The application period will end on 31st July and it can take a little time to get yourself sorted so if you are interested now is the time to take action.

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I’ve had a number of enquiries recently about how to calculate the standard error of measurement (SEM) for a range of different repeatability studies. This has struck me as odd because in my mind the SEM is a simple and clearly defined measure and given this it seems quite obvious to me how to calculate it.

On looking at a range of text books though I think I can see what the problem is. As I’ve pointed out in a previous post the SEM is almost always presented as a derivative of the intra-class correlation coefficient (ICC). Portney and Watkins for example introduce it through the formula SEM = SD√(1-ICC). For those not used to maths this looks bad enough on its own. When they probe a little further, however, they will find that the ICC itself is an esoteric output from a specifically structured ANOVA. No wonder so many give up and assume that the SEM is the rather abstract product of some largely incomprehensible calculations.

But nothing could be further from the truth. The SEM is simply the standard deviation of a number of measurements made on the same person. Bland and Altman actually recommend that it should be referred to as the within-subject standard deviation to make this clear (although I think SEM is so well established now that this is a battle not worth fighting). If you understand what a standard deviation is and how it represents variability on measurements from different people (and everyone the most basic interest in clinical measurement really should) then you should also understand what the SEM is and hown it represents variability within measurements taken on the same person. In a very real sense it is the SEM that is the primary measure of repeatability and the ICC should be seen as a derivative of it rather than vice versa.

Most importantly if you know how to calculate a standard deviation (either with a pencil and paper, calculator, or spreadsheet) then you already know how to calculate the SEM. You just use the same equation to calculate the SD of a number of measurements made on the same person rather than the those made on a number of different people. If the measurements have been made by a number of different assessors working in a particular gait lab then the SEM can be taken as representative of the lab as a whole. If they have all been made by the same assessor then they are only really valid when that individual is making the measurements.

If you make measurements on more than one person (and you should in any well designed repeatability study) then you can calculate the within-subject standard deviation for each person and you will find that this varies a little from person to person. This is where the only mildly complicated step comes in the calculations in that the overall SEM is the root mean square average of these within subject standard deviations (rather than the simple arithmetic mean).

Just to show how straightforward the calculations are I’ve prepared a document outlining how to do the sums which you can download at this link. All the data, figures and calculations for the examples are also available in these two Excel spreadsheets (here and here). If you want to listen to a more general talk about repeatability studies then there is one on my YouTube channel which uses the same examples. This is a recording of an open virtual classroom giving publicity to our MSc in Clinical Gait Analysis by distance learning so you’ll have to listen to a couple of minutes sales pitch before you get to the interesting bit!

PS Apologies to some of my recent students who probably wish they had had access to these resources a long time ago!